Research Activities

Design of a Friction Damper System for Retrofit of Gravity Load Design
RC Frames

by R. Rao and R. White

This article presents research resulting from NCEER's Building Project, to evaluate
the earthquake performance of gravity load designed structures and to determine retrofit
schemes for these structures. It is dedicated to the memory of Professor Peter Gergely, a
long-time leader in NCEER and Chairman of Dr. Rao's Ph.D. committee, up to July 1995. More
information about this study is available in a forthcoming NCEER technical report by the
authors entitled Retrofit of Non-Ductile Reinforced Concrete Frames Using Friction
Dampers, NCEER-95-0020. Comments and questions should be directed to Richard White,
Cornell University, at (607) 255-6497; fax: (607) 255-4828; email:
dick_white@qmcee.mail.cornell.edu.

Many retrofit schemes have been developed for upgrading the seismic performance of
reinforced concrete (RC) frame buildings originally designed for gravity loads (referred
to hereafter as GLD frames). Among the newer approaches are the use of supplemental
damping devices such as friction, viscous, or viscoelastic dampers. Many of these devices
have been evaluated by Professor Andrei Reinhorn and his colleagues at the University at
Buffalo.

Friction dampers show substantial promise for improving the seismic resistance of these
rather flexible structures, but there is a need for a simplified design approach. A study
at Cornell University is developing such a design methodology and aspects of this work are
described in this article including:

Description of the physical aspects of the damper system

Discussion of the effects of friction dampers on structural response

Summary of the design parameters and performance criteria

Comments on the inelastic demand spectrum method

Illustration of the methodology with a case study of a damper retrofit system design
based on a three-story GLD RC frame with dimensions and details representative of existing
structures in the central and eastern United States.

The details of this NCEER-sponsored research study are given in Rao (1996) and Rao et
al., (1995), with an extended summary in Rao et al., (1996).

Damper System

The friction damper system used in this study consists of the friction unit (cold steel
plates rubbing against clutch-lining pad material), clamped together by one or more bolts,
and a structural system for integrating the friction unit with the structure. The
structural system can be either steel braces bolted to corner regions of the open bay
space in the frame, or an infill wall with gaps around the edges to prevent stiffness
interaction of the wall with the frame members.

The installation strategy adopted here was to use a masonry infill wall with gaps
around the sides and top of the wall, with the friction unit installed between the top of
the wall and a beam spanning between columns at the top of the open bay of the frame, as
shown in figure 1. This system has the
advantage of needing only simple compression-type connections between the damper and the
frame, with little or no drilling required (and hence no noise or dust problems) for
anchorage of tension/shear connections required for normal steel bracing systems.

Effects of Friction Dampers on Structural Response

The incorporation of a friction damper system into a structural frame increases the
stiffness of the structure until a certain shear level is reached, at which point the
dampers can be set to slip, hence limiting the base shear demand on the foundations. Also,
the appropriate slip level can be selected to give the optimum response for the given
design earthquake loading. The energy dissipated by a friction damper reduces the energy
demand on the structure and damps the structural response. A friction damper system
changes the displacement characteristics and the shear demands on the structure with a
strong dependency on the frequency content of the ground motion.

The primary advantage of the friction damper approach is that much of the hysteretic
energy is dissipated by friction rather than by damage within the members of the frame.

Design Parameters and Performance Criteria

Critical design parameters include the design ground motions, the number of friction
devices, their placement within the structure, the method of attachment of the dampers to
the frame, and the load at which each damper slips.

The seismic loading and desired performance criteria are based on substantial damage
control (peak interstory drift of 1% or less) for a 500 year return period earthquake, and
collapse prevention (peak interstory drift of 4% or less) for a 2500 year earthquake. It
is suggested that the dampers be designed for the 500 year earthquake and then checked for
the 2500 year earthquake.

Inelastic Demand Spectrum Method

Several multi-degree of freedom nonlinear time history analyses, each for a different
slip load setting of the dampers, would be required to obtain the design value of the
damper slip load. A simplified approach is described here; the interested reader is
referred to Rao (1996) and Rao et al., (1995, 1996) for more details. In summary, the
method begins with a pushover analysis of the frame to obtain the capacity curve.
The force distribution used for the pushover analysis must incorporate the various modes
of vibration (first mode is sufficient for low-rise structures). At each stage of the
analysis, the floor displacements and column shears are converted to spectral
displacements (Sd) and spectral accelerations (Sa). The structure is pushed to incipient
collapse, with frame stiffness properties being continuously modified with plastic hinges
inserted into the frame as they occur. The resulting plot of Sa vs. Sd provides the capacity
curve. This capacity curve can be viewed as the envelope of secant responses of
an equivalent single-degree-of-freedom (SDOF) system. For typical RC frames, it can be
approximated with a bilinear plot.

The demand on the system can be calculated by performing a time history analysis
on an equivalent bilinear SDOF system, approximated from the capacity curve. In order to
obtain the response of the retrofitted structure for different damper slip load settings,
time history analyses can be performed on a series of bilinear SDOF systems with different
yield levels and initial stiffness corresponding to pre-slip stiffness of the retrofitted
frame. When the maximum responses are plotted on the Sa-Sd plane and connected, the inelastic
demand spectrum curve is obtained. Use of the inelastic demand spectrum curve to
obtain the design slip load is illustrated in the next section.

Case Study: Retrofit of a 3-Story GLD RC Frame

The design case study utilizes a three-story, three-bay GLD reinforced concrete frame
located on a stiff soil in Zone 3. The Kern County 1952 (Taft) earthquake recorded ground
motion time history was scaled such that the response spectrum matches the appropriate
design spectrum in the period of interest, resulting in peak ground acceleration (PGA)
values of 0.262g and 0.485g, respectively, for the ground
motions corresponding to 500 year and 2500 year return period. Nonlinear time-history
analysis using IDARC showed that the as-built structure was not able to meet the
performance criteria for the two design loading levels when the structure was subjected to
500 and 2500 year scaled Taft ground motions.

The demand spectrum curve was constructed by carrying out time history analyses of a
series of bilinear SDOF systems with different yield levels and initial stiffness
corresponding to the pre-slip stiffness of the retrofitted frame. From the demand
spectrum, the bilinear capacity curve which gives the optimum response and also satisfied
the drift limits and maximum base shear limits was obtained (figure 2).

The design slip load setting in the dampers can be calculated from the optimum capacity
curve (See Rao (1996) for details).

The part of the base shear resisted by the dampers is calculated by subtracting the
base shear in the frame from the total base shear; this is the shear level in the first
story wall at which the dampers slip. The distribution of slip forces in each story is
then set proportional to the shears developed in each story from a lateral loading with
triangular distribution. This procedure results in slip forces of 15.0 kips, 12.6 kips,
and 7.6 kips in stories 1, 2, and 3, respectively.

The adequacy of the design slip values was checked by doing several time history
analyses on the three-story frame using different slip load levels. Figure 3 shows that the design slip load distribution given above
is indeed an
optimum distribution, and leads to acceptable drift and shear levels for the 500 and 2500
year Taft earthquake loadings. Results in figure
4 show that for both levels of loading, the retrofitted structure met the target
performance criteria.

Conclusion

This article presents a design methodology for a retrofit scheme utilizing friction
dampers in frame structures. The design approach utilizes the inelastic demand spectrum
method for obtaining the design values of damper slip loads, thus avoiding the need to do
multiple inelastic time history analyses. The approach can be extended to account for
multiple ground motions.

Rao et al., (1995, 1996) also contains a design example for the retrofit of a ten-story
nonductile reinforced concrete frame.